With the newish East Midlands airspace, do EM prefer a call or (like Stansted) are they happy for you to transit from the South below 1500 feet?
My experience is that they're usually happier if they know who you are and what you're up to even if you're not planning on going into their airspace. EMA do seem to get some zone busts these days and whilst they seem to be fairly relaxed about most of them its still better not to do it - beware the new airspace if you only "think" you know it, especially as upper airspace now extends right up to the EGNA ATZ.
As has already been said, EMA also are accommodating to transits when that's possible - most direct route from the south would be through the Shepshed/Long Eaton lanes as mentioned - but if you go up the east side beneath the class delta I suggest you give them a call anyway once past Leicester AD or west abeam Leicester city if you're that side (up to then talking to Coventry may be wise given the possibility of 737s in the open FIR). Routing to the east, EMA may well give you a squawk and often ask for a call east abeam the extended centreline. A couple of other thoughts - if you do go up the east side, beware Nottingham/Tollerton's ATZ at the north east corner of EMA's airspace, and I'd also suggest that routing from vicinity of Tollerton direct to Hucknall could be difficult to justify in a single!
Andy